Yes, the mat goes on top of the clothes, and below the rim of the spin tub. When it's properly in place, it catches under the rim such that a uniformly applied pressure from below (i.e. clothes trying to escape) will not cause it to pop out, but you can remove it by bending it slightly so it can be pulled back out from under the rim. Very clever, actually.
And if you don't use it, you will have socks escape and get caught between the spinner and the outer tub, which could damage the machine. Not speaking from experience here, but it stands to reason.
Chester: but y'all in the UK have relatively *quiet* portable cement mixers, with enclosed driveline instead of an exposed ring gear like we have in the USA

(Word to the wise: wear hearing protectors, especially if you're pouring concrete in an indoor location, and keep your hair tied back or wear a cap.)
Someone back there, re. RPMs.: The UK and Euro spinners tend to be rated at 3200 rpm. The ones in the USA market tend to be rated at 1600 rpm. This may be due to the difference between a 240-volt motor (UK & Euro) and a 120-volt motor (USA). However in my experience, 1600 rpm does a dandy job, and gets a measurable amount more water out of a load.
Chester again: Yes, exactly as you said, load the stuff as if there's an agitator in the middle, and then drop the small items like socks into the "donut hole" where the "imaginary agitator" would be. (Do this a few times and it becomes second nature.)
Another thing you'll notice when you're using a spinner on all your wash, is that your dryer times are reduced by 50% to 75%. And you'll notice a difference on your electric bill as a result. Those Asian-made spinner units should pay for themselves in about a year this way, and everything after that is clear savings.
What we need in the US is a spinner with a pump and discharge hose, that can be more or less permanently installed in the laundry room. I suspect that the minor inconvenience of having to deal with manual drains on most of these units, is holding back sales. But add a drain pump, and the savings on utility bills would be enough to make these things sell themselves.